Least Common Multiple of 42 and 66

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 42 and 66 the smallest integer that is 462 that is divisible by both numbers.

Least Common Multiple (LCM) of 42 and 66 is 462.

LCM(42,66) = 462

LCM of 42 and 66

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 42 and 66

LCM of 42 and 66 is 462

Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 66. First we will calculate the prime factors of 42 and 66.

Prime Factorization of 42


2 42
3 21
7 7
1

Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:

42 = 21×31×71

Prime Factorization of 66


2 66
3 33
11 11
1

Prime factors of 66 are 2, 3,11. Prime factorization of 66 in exponential form is:

66 = 21×31×111

Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 66.

LCM(42,66) = 21×31×71×111
LCM(42,66) = 462

Factors of 42

List of positive integer factors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42

Factors of 66

List of positive integer factors of 66 that divides 66 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66

Least Common Multiple of 42 and 66 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 66, than apply into the LCM equation.

GCF(42,66) = 6
LCM(42,66) = ( 42 × 66) / 6
LCM(42,66) = 2772 / 6
LCM(42,66) = 462

Properties of LCM 42 and 66

(i) The LCM of 66 and 42 is associative

LCM of 42 and 66 = LCM of 66 and 42

Related Least Common Multiples of 42

Related Least Common Multiples of 66

Frequently Asked Questions on LCM of 42 and 66

1. What is the LCM of 42 and 66?

Answer: LCM of 42 and 66 is 462.

2. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

3. What are the Factors of 66?

Answer: Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. There are 8 integers that are factors of 66. The greatest factor of 66 is 66.

4. How to Find the LCM of 42 and 66?

Answer:

Least Common Multiple of 42 and 66 = 462

Step 1: Find the prime factorization of 42

42 = 2 x 3 x 7

Step 2: Find the prime factorization of 66

66 = 2 x 3 x 11

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 462 = 2 x 3 x 7 x 11

Step 4: Therefore, the least common multiple of 42 and 66 is 462.